'Square Corners' printed from http://nrich.maths.org/

On each of these grids the counters lie at the four corners of a
square:

What is the greatest number of counters you can place on the
grid below without four of them lying at the corners of a
square?

This problem is taken from
'Mathematical Challenges for Able Pupils Key Stages 1 and 2',
published by DfES. You can find out more about this book, including
how to order it, on the Standards website
here.